 Okay, hi everyone, I'll talk today about some work that I did as part of my PhD in Princeton. I'll start with an older project that's been published for a while and then I'll move on to some new stuff that's not out there yet, but I think will hopefully be of interest to some of the people in this crowd. The focus of the talk is going to be on self-assembled. So this term self-assembly I think is defined quite differently depending on the discipline. But in terms of the social insect world, we're really just talking about structures that are formed out of the bodies of insects when they join themselves together. And in certain cases, these can be considered as almost like intermediate level parts of insect societies. And in particular, the structures that I'm going to be talking about are the really functional adaptive units. So they're not just sort of a ball of ants, but they serve some purpose for the colony. And just to kind of visualize that a bit, this is a diagram of a swarm raid of one of the army ant species that I'm going to talk about. So I'll talk about two different species of acetone and acetone berycheli and acetone hamedum. And this is just a kind of a zoomed out aerial view diagram of a daily swarm raid of one of these species. And so these raids can stretch for hundreds of meters across the rainforest floor. And you'll see at the front of the swarm, along the front of the swarm, this is where the actual raiding is happening, just the death and destruction and mayhem as these predatory ants are raiding through the leaf litter. And then they're dismembering that prey and carrying it back along this trail network. And what I've labeled here with these different colors are where we might imagine some of these self-assembled structures to occur. And so these can be of all different scales from the smallest scale of just one individual ant filling a small hole to the slightly larger bridges and scaffolds that I'm going to talk about today. And these are dispersed throughout this, again, huge network. So when I refer to these things as intermediate level parts, this is kind of what we're talking about. And this is an example of bridge structure that you might see if you run into one of these army ant swarms. So all the field work that I'm going to talk about today was done in Panama on Barrow, Colorado Island. And this first project was a close collaboration between me and Chris Reed, whom some of you may know. So you'll notice going across this bridge, there's some ants carrying prey items and there's bi-directional traffic. So there's ants flowing out from the Bivouac, out to the raid front, and there's ants carrying prey back along the trail. And so the first question we wanted to ask about these bridges, just based on our observations, was do they function as shortcuts in a way? So before we did this work, I wasn't really known what the function of these structures were. But we had an idea that if we built this apparatus, where we forced the ants to go up off of their trail, divert around this obstacle, that they might start bridging around the corner, and then over time that bridge might move down to create a kind of a shortcut. And indeed, that's what we found with this experiment. It worked out really nicely. You'll see the bridge starts to form in the upper corner here. And then over the course of, this was a 15 minute experiment, over the course of the experiment, the bridge moves down to create a shortcut. And so yeah, they do move. Interestingly enough, they move at different distances, depending on the size of that angle. So we could adjust the apparatus to different angle conditions. And so you can see here, the bridges move the farthest at these very small angles, whereas when the angle is much wider, they didn't really move that much at all. And so we wondered, why would this be the case? And what we found, when we started to think about the cost and benefits of these structures, is that at the wider angles, to create the same length of a shortcut, you really have to put a lot more workers into the structure. And so what we found is that the bridges actually moved down only to a point at which there was this trade off between the benefits of the shortcut and the costs of locking up additional workers in the structure. So that was kind of cool, and we consider this to be a kind of collective computation. So here the output at the group level is this formation of a bridge and computing how far it moves down. And the input is just coming from these individual level sensors of these ants. And in this case, we don't really know what exactly they're sensing. That's causing these bridges to form. We have some ideas, and this is sort of ongoing work. But in this case, the mapping between these two is kind of uncertain. We don't really know how you get from this individual level sensing to this group level output. And so that brings me to the next project, and this is all new work now. And this was inspired by something that I saw in my first field season. In Panama, this is just on the side of one of the dorm buildings on BCI. And you can see these army ants are raiding. This is a sort of electrical box where maybe there's some wasp nest in their raiding in there. And then you can see that a bunch of ants have just stopped along this wall to form this kind of what we're calling a scaffolding structure. And so we saw this and we were like, that's crazy. What's going on? And so that inspired this next series of experiments that I'm gonna talk about. So we designed here a similar apparatus as the last kind. Except in this case, we have this adjustable vertical surface in the middle. But we did sort of same kind of method in that we found this existing raiding trail, stopped the traffic, which is pretty difficult to do, inserted the apparatus. And then tried to get the ants to go back up, reform the trail over the apparatus, which is a lot more difficult than it sounds, unfortunately. And so we had eight different angle treatments. And this is what the apparatus looks like in action. So yeah, you can see here, this is the scaffolding structure that I'm gonna talk more about, and in this case, the angle's quite steep. So you have a nice robust structure that's formed there. And so we took a bunch of videos, about ten different experiments at each of those angle treatments. And in order to extract the data, basically the main thing that we're trying to measure is the size of the structure and how it grows over time. And so we just developed an automated method using some image attraction to just try to get rid of the moving ants and figure out who's actually stationary. And that becomes the size of the structure that we're measuring. And so this is just the raw data, like first 30 seconds of one of these experiments. So again, the experiment was started as soon as the traffic starts flowing again over the apparatus. And you can see already some ants are falling off, some ants are slipping. But a few will start to stop and become the beginnings of this scaffolding structure. And it does actually happen quite quickly. You'll see even within the first 30 seconds. And again, this is back to the beginnings. You can see how quickly that forms. And so this is just all the data for all of the experiments for each angle. And you can see just kind of intuitively that larger structures form at the steeper angles. So down in the right-hand corner, you have all the experiments for 90 degrees, which is completely vertical. And then at these lower angles, where you're basically almost horizontal, there's pretty much no structures forming at all until you get to somewhere around 40 or 50 degrees. And this is just so you can see a little bit better what's going on. There's 10 different trials plotted here, all at 90 degrees. And again, on the y-axis here, we're just measuring the size of the scaffolding structure as measured by number of ants. So that seemed to be a useful way to quantify those. So this data looks great, looks really cool. But we're wondering now what actually drives the growth of these structures. And so if the response variable is just this final size of the structure, this was the sort of first analysis that we did. These are maybe some possible predictors that could influence that. And what we expected to find based on our previous work was that the traffic flow rate would be a really important factor in determining the final size of these structures. And of course, the angle of the surface seems to be very important. So again, this is just now plotting for each angle, the size of the structures that formed. And so we did find that angle is the most important factor. And kind of surprisingly, rather than traffic rate, it was the rate of prey delivery that was also another significant effect that we found. And here's just kind of a rough visualization of the relationship between the prey delivery rate, which is just measured as number of ants carrying prey per second and the final size of the structure. Cool, so here's another experiment. This one's sped up a bit. This is now an entire 10 minute experiment at 30 time speed. So you can see how quickly this really quite robust structure forms. And when you see these things sped up, it really, I think, inspires at least me to think about different applications of this system, different types of analogies. And to me, it reminds me a lot of the process of wound healing, or some self healing material. So that's, hopefully I'll be able to talk to some of you here about that, who have more expertise in those areas. But again, we see this as another kind of a collective computation, where here we have this output at the group level. In this case, it's the growth of these scaffold structures. And in this case, we know what the input is from the individual level sensors, because we can see the ants slipping. So there's clearly some individual level error, some individual level sensing that's going on. And so I think it's going to be much easier to extract the mapping in this case. So with that in mind, I developed a simple model of how these structures might grow, and it's based on the concept of a proportional controller. So this is a simple form of control driven by negative feedback, where the controller response is proportional to the strength of some error signal. And a good example would be like cruise control in a car. And so this is just a really basic kind of generic model, where you have this error term times some gain, which is like just a tuning parameter. And the error is just the difference between some set point minus the present value of whatever the system is trying to optimize for. So I was wondering, okay, in this case, what is the system level response? Let's say we're just going to call it scaffolding formation, because that's the thing that's forming to correct for some error. What's the individually sensed error? It's some traffic disruption due to the ant slipping as they walk across the surface. And so those are my two things. We have a overall scaffold size, and in this case, instead of an error, I'm just calling this the probability of slipping, because that's what the error is being sensed. And so in order to get that probability of slipping, it's actually quite easy, because all we need to do if we have this growth curve, we know how many ants are joining and leaving the structure at any given time. And so if we just take that number of ants joining as a proportion of the traffic, that gives us this probability of stopping p s. And so with those things, we can just write this really simple set of couple differential equations that give us the change in scaffold size over time, and they give us also the change of this probability of slipping over time, which again, is being reduced in proportion to the size of the structure. So that's this proportional control idea. And we only now have two free parameters that we need to worry about, because this mu parameter is just basically the eligible ants. So all the traffic minus the prey, minus those carrying prey, because they can't stop. And so we need to now estimate this beta parameter, which is related to that gain or tuning parameter, and this initial probability of stopping, which we can estimate from the data. So just real quick to walk through that again. So the rate of scaffold growth at time t is given by this. Current probability of stopping times the number of eligible ants. And then probability of stopping at t is being reduced in proportion to the size of the scaffold. Yeah, so this is kind of ongoing work now. I'm just now fitting this data to extract these estimated parameters, okay? So I'm just going through this process of fitting the model to the data. It looks pretty good. Now I'm just trying to figure out how to interpret these parameters that I'm getting out. So again, if I go back just a few slides, I know that both of these are gonna be a function of the prey rate and the angle, because these are the important factors that kind of determine the structure size. So I'm trying to now see, okay, if I look at the probability of stopping, that seems to increase with the angle, which makes sense. As the angle gets steeper, your initial probability of stopping is also gonna increase. And then this tuning parameter beta seems to be higher at these lower angles. And here I'm just looking at the data for the angles from 50 and above, because below that, nothing's really happening. So then I'm also trying to see if there's any relationship between this prey, delivery rate and these parameters. Definitely doesn't look like anything going on with this beta, but maybe the probability of stopping is also related to the prey coming through. So yeah, I think this again is a really nice example of a very tractable kind of collective computation, where now we know the mapping, and we know that it's this individual error correction that is driving this group level output. And I'm calling this a form of distributed proportional control, because there's no one sort of overseer that's controlling all this. So just to recap a few conclusions, the angle of the substrate and the amount of prey transported seem to be the most significant predictors of the final size. And just a really simple model of these two couple differential equations seems to be able to describe the growth of these structures pretty well, which is nice. And yeah, just generally, as we kind of already know, our mints can perform really sophisticated computations at the group level, but only taking in this individual level sensing. So here's just another video for the road. This one's really sped up, so you can really see that kind of dynamics of the process. And it would be great to talk to anyone who's interested in thinking about different applications for this model or these data. I think there's so many potential applications in swarm robotics. If we can figure out just some simple way to implement this algorithm in a robotic system. And the nice thing about this last project is that it doesn't even need to be explicitly self-assembling, because you could have robots that just stop along a substrate somehow. And I think this could be also important for control of autonomous vehicles, other kinds of traffic problems, design of self-healing materials, and just any other general phenomenon involving aggregative growth. And that's it. We'll take any questions. Thank you.